Time | Items |
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All day |
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4:00pm |
04/22/2024 - 4:00pm This talk will be about joint work with Baldi, Miller, and Ullmo that uses dynamics and/or Hodge theory to study rigidity problems for representations of real and complex hyperbolic lattices, especially those with many properly immersed totally geodesic subspaces (which are among the most well-studied lattices). Very roughly, rich representations are those for which the image of the representation has an action that respects this abundant collection of subgroups in some way, for instance the homomorphism induced by a map f : M -> N where infinitely many properly immersed totally geodesic subspaces of M map into a properly immersed totally geodesic subspace of N. The geometric motivation for defining rich representations has appeared in previous work of several people in several contexts. I will describe settings where we can show that rich representations are superrigid, including some progress toward a question of Siu about whether holomorphic embeddings between higher-dimensional complex hyperbolic manifolds must be totally geodesic.
Location:
KT205
04/22/2024 - 4:30pm The Bethe subalgebras of the Yangian Y(gl(n)) form a family of maximal commutative subalgebras indexed by points of the Deligne-Mumford compactification of the moduli space M(0,n+2). When considering a point C in the real locus of this parameter space, the corresponding Bethe subalgebra B(C) acts with simple spectrum on a given tame representation of Y(gl(n)). This results in an unramified covering, whose fiber over C is the set of eigenlines for the action of B(C). I will discuss the identification of each fiber with a collection of Gelfand-Tsetlin keystone patterns, which carry a gl(n)-crystal structure, as well as the monodromy action realized by a type of cactus group. This is joint work with Anfisa Gurenkova and Leonid Rybnikov. Location:
KT217
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Links
[1] https://math.yale.edu/calendar/grid/day/2024-04-21?field_calendar_tags_tid_selective=46
[2] https://math.yale.edu/calendar/grid/day/2024-04-23?field_calendar_tags_tid_selective=46
[3] https://math.yale.edu/event/rich-representations-and-superrigidity
[4] https://math.yale.edu/event/bethe-subalgebras-yangian-gln-tame-representations-and-cacti
[5] https://math.yale.edu/print/list/calendar/grid/day/2024-04-22
[6] webcal://math.yale.edu/calendar/export.ics